Paul Expert

Uncovering space-independent communities in spatial networks

Many complex systems are organized in the form of a network embedded in space. Important examples include the physical Internet infrastucture, road networks, flight connections, brain functional networks, and social networks. The effect of space on network topology has recently come under the spotlight because of the emergence of pervasive technologies based on geolocalization, which constantly fill databases with people’s movements and thus reveal their trajectories and spatial behavior. Extracting patterns and regularities from the resulting massive amount of human mobility data requires the development of appropriate tools for uncovering information in spatially embedded networks. In contrast with most works that tend to apply standard network metrics to any type of network, we argue in this paper for a careful treatment of the constraints imposed by space on network topology. In particular, we focus on the problem of community detection and propose a modularity function adapted to spatial networks. We show that it is possible to factor out the effect of space in order to reveal more clearly hidden structural similarities between the nodes. Methods are tested on a large mobile phone network and computer-generated benchmarks where the effect of space has been incorporated.

Traumatic brain injury impairs small-world topology

Objective: We test the hypothesis that brain networks associated with cognitive function shift away from a “small-world” organization following traumatic brain injury (TBI). Methods: We investigated 20 TBI patients and 21 age-matched controls. Resting-state functional MRI was used to study functional connectivity. Graph theoretical analysis was then applied to partial correlation matrices derived from these data. The presence of white matter damage was quantified using diffusion tensor imaging. Results: Patients showed characteristic cognitive impairments as well as evidence of damage to white matter tracts. Compared to controls, the graph analysis showed reduced overall connectivity, longer average path lengths, and reduced network efficiency. A particular impact of TBI is seen on a major network hub, the posterior cingulate cortex. Taken together, these results confirm that a network critical to cognitive function shows a shift away from small-world characteristics. Conclusions: We provide evidence that key brain networks involved in supporting cognitive function become less small-world in their organization after TBI. This is likely to be the result of diffuse white matter damage, and may be an important factor in producing cognitive impairment after TBI.

Homological scaffolds of brain functional networks

Networks, as efficient representations of complex systems, have appealed to scientists for a long time and now permeate many areas of science, including neuroimaging (Bullmore and Sporns 2009 Nat. Rev. Neurosci. 10, 186–198. (doi:10.1038/nrn2618)). Traditionally, the structure of complex networks has been studied through their statistical properties and metrics concerned with node and link properties, e.g. degree-distribution, node centrality and modularity. Here, we study the characteristics of functional brain networks at the mesoscopic level from a novel perspective that highlights the role of inhomogeneities in the fabric of functional connections. This can be done by focusing on the features of a set of topological objects—homological cycles—associated with the weighted functional network. We leverage the detected topological information to define the homological scaffolds, a new set of objects designed to represent compactly the homological features of the correlation network and simultaneously make their homological properties amenable to networks theoretical methods. As a proof of principle, we apply these tools to compare resting-state functional brain activity in 15 healthy volunteers after intravenous infusion of placebo and psilocybin—the main psychoactive component of magic mushrooms. The results show that the homological structure of the brains functional patterns undergoes a dramatic change post-psilocybin, characterized by the appearance of many transient structures of low stability and of a small number of persistent ones that are not observed in the case of placebo.

Self-similar correlation function in brain resting-state functional magnetic resonance imaging.

Adaptive behaviour, cognition and emotion are the result of a bewildering variety of brain spatio-temporal activity patterns. An important problem in neuroscience is to understand the mechanism by which the human brains 100 billion neurons and 100 trillion synapses manage to produce this large repertoire of cortical configurations in a flexible manner. In addition, it is recognized that temporal correlations across such configurations cannot be arbitrary, but they need to meet two conflicting demands: while diverse cortical areas should remain functionally segregated from each other, they must still perform as a collective, i.e. they are functionally integrated. Here, we investigate these large-scale dynamical properties by inspecting the character of the spatio-temporal correlations of brain resting-state activity. In physical systems, these correlations in space and time are captured by measuring the correlation coefficient between a signal recorded at two different points in space at two different times. We show that this two-point correlation function extracted from resting-state functional magnetic resonance imaging data exhibits self-similarity in space and time. In space, self-similarity is revealed by considering three successive spatial coarse-graining steps while in time it is revealed by the 1/f frequency behaviour of the power spectrum. The uncovered dynamical self-similarity implies that the brain is spontaneously at a continuously changing (in space and time) intermediate state between two extremes, one of excessive cortical integration and the other of complete segregation. This dynamical property may be seen as an important marker of brain well-being in both health and disease.

Cerebral energy metabolism and the brain's functional network architecture: an integrative review.

Recent functional magnetic resonance imaging (fMRI) studies have emphasized the contributions of synchronized activity in distributed brain networks to cognitive processes in both health and disease. The brain’s ‘functional connectivity’ is typically estimated from correlations in the activity time series of anatomically remote areas, and postulated to reflect information flow between neuronal populations. Although the topological properties of functional brain networks have been studied extensively, considerably less is known regarding the neurophysiological and biochemical factors underlying the temporal coordination of large neuronal ensembles. In this review, we highlight the critical contributions of high-frequency electrical oscillations in the γ-band (30 to 100 Hz) to the emergence of functional brain networks. After describing the neurobiological substrates of γ-band dynamics, we specifically discuss the elevated energy requirements of high-frequency neural oscillations, which represent a mechanistic link between the functional connectivity of brain regions and their respective metabolic demands. Experimental evidence is presented for the high oxygen and glucose consumption, and strong mitochondrial performance required to support rhythmic cortical activity in the γ-band. Finally, the implications of mitochondrial impairments and deficits in glucose metabolism for cognition and behavior are discussed in the context of neuropsychiatric and neurodegenerative syndromes characterized by large-scale changes in the organization of functional brain networks.

The brain's code and its canonical computational motifs. From sensory cortex to the default mode network: A multi-scale model of brain function in health and disease

A variety of anatomical and physiological evidence suggests that the brain performs computations using motifs that are repeated across species, brain areas, and modalities. The computational architecture of cortex, for example, is very similar from one area to another and the types, arrangements, and connections of cortical neurons are highly stereotyped. This supports the idea that each cortical area conducts calculations using similarly structured neuronal modules: what we term canonical computational motifs. In addition, the remarkable self-similarity of the brain observables at the micro-, meso- and macro-scale further suggests that these motifs are repeated at increasing spatial and temporal scales supporting brain activity from primary motor and sensory processing to higher-level behaviour and cognition. Here, we briefly review the biological bases of canonical brain circuits and the role of inhibitory interneurons in these computational elements. We then elucidate how canonical computational motifs can be repeated across spatial and temporal scales to build a multiplexing information system able to encode and transmit information of increasing complexity. We point to the similarities between the patterns of activation observed in primary sensory cortices by use of electrophysiology and those observed in large scale networks measured with fMRI. We then employ the canonical model of brain function to unify seemingly disparate evidence on the pathophysiology of schizophrenia in a single explanatory framework. We hypothesise that such a framework may also be extended to cover multiple brain disorders which are grounded in dysfunction of GABA interneurons and/or these computational motifs.

Functional brain networks before the onset of psychosis: A prospective fMRI study with graph theoretical analysis

Individuals with an at-risk mental state (ARMS) have a risk of developing a psychotic disorder significantly greater than the general population. However, it is not currently possible to predict which ARMS individuals will develop psychosis from clinical assessment alone. Comparison of ARMS subjects who do, and do not, develop psychosis can reveal which factors are critical for the onset of illness. In the present study, 37 patients with an ARMS were followed clinically at least 24 months subsequent to initial referral. Functional MRI data were collected at the beginning of the follow-up period during performance of an executive task known to recruit frontal lobe networks and to be impaired in psychosis. Graph theoretical analysis was used to compare the organization of a functional brain network in ARMS patients who developed a psychotic disorder following the scan (ARMS-T) to those who did not become ill during the same follow-up period (ARMS-NT) and aged-matched controls. The global properties of each groups representative network were studied (density, efficiency, global average path length) as well as regionally-specific contributions of network nodes to the organization of the system (degree, farness-centrality, betweenness-centrality). We focused our analysis on the dorsal anterior cingulate cortex (ACC), a region known to support executive function that is structurally and functionally impaired in ARMS patients. In the absence of between-group differences in global network organization, we report a significant reduction in the topological centrality of the ACC in the ARMS-T group relative to both ARMS-NT and controls. These results provide evidence that abnormalities in the functional organization of the brain predate the onset of psychosis, and suggest that loss of ACC topological centrality is a potential biomarker for transition to psychosis.

Entangled communities and spatial synchronization lead to criticality in urban traffic

Understanding the relation between patterns of human mobility and the scaling of dynamical features of urban environments is a great importance for todays society. Although recent advancements have shed light on the characteristics of individual mobility, the role and importance of emerging human collective phenomena across time and space are still unclear. In this Article, we show by using two independent data-analysis techniques that the traffic in London is a combination of intertwined clusters, spanning the whole city and effectively behaving as a single correlated unit. This is due to algebraically decaying spatio-temporal correlations, that are akin to those shown by systems near a critical point. We describe these correlations in terms of Taylors law for fluctuations and interpret them as the emerging result of an underlying spatial synchronisation. Finally, our results provide the first evidence for a large-scale spatial human system reaching a self-organized critical state.

MENGA: A New Comprehensive Tool for the Integration of Neuroimaging Data and the Allen Human Brain Transcriptome Atlas

Introduction Brain-wide mRNA mappings offer a great potential for neuroscience research as they can provide information about system proteomics. In a previous work we have correlated mRNA maps with the binding patterns of radioligands targeting specific molecular systems and imaged with positron emission tomography (PET) in unrelated control groups. This approach is potentially applicable to any imaging modality as long as an efficient procedure of imaging-genomic matching is provided. In the original work we considered mRNA brain maps of the whole human genome derived from the Allen human brain database (ABA) and we performed the analysis with a specific region-based segmentation with a resolution that was limited by the PET data parcellation. There we identified the need for a platform for imaging-genomic integration that should be usable with any imaging modalities and fully exploit the high resolution mapping of ABA dataset. Aim In this work we present MENGA (Multimodal Environment for Neuroimaging and Genomic Analysis), a software platform that allows the investigation of the correlation patterns between neuroimaging data of any sort (both functional and structural) with mRNA gene expression profiles derived from the ABA database at high resolution. Results We applied MENGA to six different imaging datasets from three modalities (PET, single photon emission tomography and magnetic resonance imaging) targeting the dopamine and serotonin receptor systems and the myelin molecular structure. We further investigated imaging-genomic correlations in the case of mismatch between selected proteins and imaging targets.

Insights into brain architectures from the homological scaffolds of functional connectivity networks

In recent years, the application of network analysis to neuroimaging data has provided useful insights about the brains functional and structural organization in both health and disease. This has proven a significant paradigm shift from the study of individual brain regions in isolation. Graph-based models of the brain consist of vertices, which represent distinct brain areas, and edges which encode the presence (or absence) of a structural or functional relationship between each pair of vertices. By definition, any graph metric will be defined upon this dyadic representation of the brain activity. It is however unclear to what extent these dyadic relationships can capture the brains complex functional architecture and the encoding of information in distributed networks. Moreover, because network representations of global brain activity are derived from measures that have a continuous response (i.e., interregional BOLD signals), it is methodologically complex to characterize the architecture of functional networks using traditional graph-based approaches. In the present study, we investigate the relationship between standard network metrics computed from dyadic interactions in a functional network, and a metric defined on the persistence homological scaffold of the network, which is a summary of the persistent homology structure of resting-state fMRI data. The persistence homological scaffold is a summary network that differs in important ways from the standard network representations of functional neuroimaging data: (i) it is constructed using the information from all edge weights comprised in the original network without applying an ad hoc threshold and (ii) as a summary of persistent homology, it considers the contributions of simplicial structures to the network organization rather than dyadic edge-vertices interactions. We investigated the information domain captured by the persistence homological scaffold by computing the strength of each node in the scaffold and comparing it to local graph metrics traditionally employed in neuroimaging studies. We conclude that the persistence scaffold enables the identification of network elements that may support the functional integration of information across distributed brain networks.